To show that consensus is achieved on dynamic networks under arbitrary switchings, we will prove that (REF ) is a common Lyapunov function for each subsystem of the switched nonlinear system (REF ) [1]}. To this aim, assume that \(\sigma (t)=l\)  for \(t\in [0,\infty )\) .
Then, it follows that
\(\dot{V}(x) = \frac{\sqrt{\lambda }\beta (\overline{m})}{\Vert \delta \Vert }\delta ^T\dot{\delta } = -\lambda \beta (\overline{m})^2V^{-1}\delta ^TD(\mathcal {X}_l)\mathcal {F}(D(\mathcal {X}_l)^T\delta ),\) 
